depth (version 2.1-1.1)

ctrmean: Centroid trimmed mean

Description

Computes the centroid of a Tukey depth-based trimmed region.

Usage

ctrmean(x ,alpha, eps = 1e-8, mustdith = FALSE, maxdith = 50, 
   dithfactor = 10 ,factor = .8)

Arguments

x

Bivariate data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one bivariate observation. If it is a list, both components must be numerical vectors of equal length (coordinates of observations).

alpha

Outer trimming fraction (0 to 0.5). Observations whose depth is less than alpha to be trimmed.

eps

Error tolerance to control the calculation.

mustdith

Logical. Should dithering be applied? Used when data set is not in general position or a numerical problem is encountered.

maxdith

Positive integer. Maximum number of dithering steps.

dithfactor

Scaling factor used for horizontal and vertical dithering.

factor

Proportion (0 to 1) of outermost contours computed according to a version of the algorithm ISODEPTH of Rousseeuw and Ruts (1998); remaining contours are derived from an algorithm in Rousseeuw et al. (1999).

Value

Centroid trimmed mean vector

Details

Dimension 2 only. Centroid trimmed mean is defined to be the centroid of a Tukey depth-based trimmed region relative to the uniform measure. Contours are derived from algorithm ISODEPTH by Ruts and Rousseeuw (1996) or, more exactly, revised versions of this algorithm which appear in Rousseeuw and Ruts (1998) and Rousseeuw et al. (1999). Argument factor determines which version to use. If \(n\) is the number of observations, contours of depth \(\le \) factor \(n/2\) are obtained from the 1998 version, while the remaining contours are derived from the 1999 version.

When the data set is not in general position, dithering can be used in the sense that random noise is added to each component of each observation. Random noise takes the form eps times dithfactor times U for the horizontal component and eps times dithfactor times V for the vertical component, where U, V are independent uniform on [-.5, 5.]. This is done in a number of consecutive steps applying independent U's and V's.

References

Masse, J.C. (2008), Multivariate Trimmed means based on the Tukey depth, J. Statist. Plann. Inference, in press.

Ruts, I. and Rousseeuw, P.J. (1996), Computing depth contours of bivariate point clouds, Comput. Statist. Data Anal., 23. 153--168.

Rousseeuw, P.J. and Ruts, I. (1998), Constructing the bivariate Tukey median, Stat. Sinica, 8, 828--839.

Rousseeuw, P.J., Ruts, I., and Tukey, J.W. (1999), The Bagplot: A Bivariate Boxplot, The Am. Stat., 53, 382--387.

See Also

med for multivariate medians and trmean for classical-like depth-based trimmed means.

Examples

# NOT RUN {
## exact centroid trimmed mean
set.seed(345)
xx <- matrix(rnorm(1000), nc = 2)
ctrmean(xx, .2)

## second example of an exact centroid trimmed mean
set.seed(159); library(MASS)
mu1 <- c(0,0); mu2 <- c(6,0); sigma <- matrix(c(1,0,0,1), nc = 2)
mixbivnorm <- rbind(mvrnorm(80, mu1 ,sigma), mvrnorm(20, mu2, sigma))
ctrmean(mixbivnorm, 0.3)

## dithering used for data set not in general position
data(starsCYG, package = "robustbase")
ctrmean(starsCYG, .1, mustdith = TRUE)
# }